A076460 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly one way.

1, 103, 1130, 6070, 22355, 64981, 160468, 351660, 703365, 1308835, 2297086, 3841058, 6166615, 9562385, 14390440, 21097816, 30228873, 42438495, 58506130, 79350670, 106046171, 139838413, 182162300, 234660100, 299200525, 377898651, 473136678, 587585530, 724227295

Offset

1,2

References

Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1)/6.

G.f.: x*(1+96*x+430*x^2+288*x^3+25*x^4)/(1-x)^7.

Maple

seq(1/6*n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1), n=1..30);

Mathematica

CoefficientList[Series[(1 + 96 x + 430 x^2 + 288 x^3 + 25 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)

Prog

(Magma) [n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013

Crossrefs

Cf. A076389, A076461-A076465.

Sequence in context: A023355 A113629 A034180 * A346499 A245495 A097726

Adjacent sequences: A076457 A076458 A076459 * A076461 A076462 A076463

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 13 2002

Extensions

More terms from Vincenzo Librandi, Dec 30 2013

Status

approved